This should do what you are looking for.
Create a sketch of the shape you want to cut. I sketched one profile, and used offset to create the second.
Use the Curve - Split command to split the model faces into different faces.
Select the new faces and use the Surface - Knit command to "stitch" them together into a single surface.
Insert - Boss - Thicken. This will add thickness to the surface body. I like to use the "both directions" option since it prevents errors related to zero thickness geometry. The thickness of this command will be the depth of the cut.
Insert - Feature - Combine - Subtract
Now subtract one body from the other.